To multiply large numbers, the distributive property is very useful. We have already seen some examples of this in base twelve, and we can use it in base ten. For example, when asked how to do 14 x 6 mentally, people often respond that they would do 10 x 6 and add 4 x 6. In effect, they broke up the 14 into 10 and 4, and multiplied each part of 14 by 6. This creates easier multiplication problems that we can use to build a "harder" multiplication problem. The formal notation would be: 14 x 6 = (10 + 4)6 = 10 x 6 + 4 x 6 = 60 + 24 = 84.
In our class, we have also seen that there is a spatial component to this. We have used arrays and what I call "pairing problems" to work on this idea. For example, to organize the ideas above spatially we worked this problem:
A meal at a local restaurant consists of one salad and one entrée. The restaurant serves 6 different kinds of salad and 14 different kinds of entrées. 10 of the entrees have meat. Use a single array to represent the total number of meals that can be made. On your array, identify the meals that contain some meat and the meals that contain no meat. POST BY LINDSEY HELLER
posting opp: Attach a file showing a picture for this problem, or insert a picture into the wiki page (no, I'm not quite sure how to do that--see if you can figure it out).
Next we thought about when both numbers of a multiplication problem get "large" (more than a base, say). There are also important spatial ideas here!
Large Multiplication
To multiply large numbers, the distributive property is very useful. We have already seen some examples of this in base twelve, and we can use it in base ten. For example, when asked how to do 14 x 6 mentally, people often respond that they would do 10 x 6 and add 4 x 6. In effect, they broke up the 14 into 10 and 4, and multiplied each part of 14 by 6. This creates easier multiplication problems that we can use to build a "harder" multiplication problem. The formal notation would be: 14 x 6 = (10 + 4)6 = 10 x 6 + 4 x 6 = 60 + 24 = 84.
In our class, we have also seen that there is a spatial component to this. We have used arrays and what I call "pairing problems" to work on this idea. For example, to organize the ideas above spatially we worked this problem:
A meal at a local restaurant consists of one salad and one entrée. The restaurant serves 6 different kinds of salad and 14 different kinds of entrées. 10 of the entrees have meat.
Use a single array to represent the total number of meals that can be made.
On your array, identify the meals that contain some meat and the meals that contain no meat.
POST BY LINDSEY HELLER
posting opp: Attach a file showing a picture for this problem, or insert a picture into the wiki page (no, I'm not quite sure how to do that--see if you can figure it out).
Next we thought about when both numbers of a multiplication problem get "large" (more than a base, say). There are also important spatial ideas here!